Information on Result #1792373
Digital (57, 69, 524296)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(869, 524296, F8, 12) (dual of [524296, 524227, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(868, 524294, F8, 12) (dual of [524294, 524226, 13]-code), using
- trace code [i] based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- trace code [i] based on linear OA(6434, 262147, F64, 12) (dual of [262147, 262113, 13]-code), using
- linear OA(868, 524295, F8, 11) (dual of [524295, 524227, 12]-code), using Gilbert–Varšamov bound and bm = 868 > Vbs−1(k−1) = 122160 317266 676120 168949 853895 131530 812716 334407 208512 651264 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(868, 524294, F8, 12) (dual of [524294, 524226, 13]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.